Substitution planar tilings with $n$-fold rotational symmetry

We prove that the Sub Rosa substitution tilings with $2n$-fold rotational symmetry defined by Kari and Rissanen are not planar for odd $n$. However we prove the existence of planar substitution tilings with $2n$-fold rotational symmetry for any odd $n$. The tilings we consider are rhombic and edge-to-edge. We give an explicit 10-fold substitution planar tiling and we give a construction method for the general case of $2n$-fold with odd $n$.